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Optimal calibration of instrumented treadmills using an instrumented pole
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Technical note
Optimal calibration of instrumented treadmills using an instrumented pole L.H. Sloot a,b,∗, H. Houdijk b,c, M.M. van der Krogt a,b, J. Harlaar a,b a
VU University Medical Center, Department of Rehabilitation Medicine, PO Box 7057, 1007 MB Amsterdam, The Netherlands Research Institute MOVE, VU University Amsterdam, Van der Boechorststraat 7, 1081 BT Amsterdam, The Netherlands c Heliomare Rehabilitation Center, Research and Development, Relweg 51, 1949 EC Wijk aan Zee, The Netherlands b
a r t i c l e
i n f o
Article history: Received 9 September 2015 Revised 14 March 2016 Accepted 11 April 2016 Available online xxx Keywords: Kinematics Biomechanics Center of pressure Kinetics Gait analysis
a b s t r a c t Calibration of instrumented treadmills is imperative for accurate measurement of ground reaction forces and center of pressure (COP). A protocol using an instrumented pole has been shown to considerably increase force and COP accuracy. This study examined how this protocol can be further optimized to maximize accuracy, by varying the measurement time and number of spots, using nonlinear approaches to calculate the calibration matrix and by correcting for potential inhomogeneity in the distribution of COP errors across the treadmill’s surface. The accuracy increased with addition of spots and correction for the inhomogeneous distribution across the belt surface, decreased with reduction of measurement time, and did not improve by including nonlinear terms. Most of these methods improved the overall accuracy only to a limited extent, suggesting that the maximal accuracy is approached given the treadmill’s inherent mechanical limitations. However, both correction for position dependence of the accuracy as well as its optimization within the walking area are found to be valuable additions to the standard calibration process. © 2016 IPEM. Published by Elsevier Ltd. All rights reserved.
1. Introduction In gait analysis, normal and pathological gait patterns are examined on the basis of joint kinematics and kinetics. The latter includes net joint moments and powers, which are calculated through inverse dynamics using a linked segment model with mass distribution, kinematics, ground reaction forces (GRF) and moments, as well as hereof derived center of pressure (COP). Of all these data, errors in GRF and thus COP have been shown to be the main source of inaccuracies in lower body kinetics [1–4]. These errors are generally larger in instrumented treadmills compared with conventional force plates that are incorporated in the floor, because of their large and compliant structure [5]. Moreover, novel applications of these treadmills, such as feedback on frontal knee moments during gait [6] or system identification of the neuromuscular system [7], require highly accurate force measurements. Recently, a protocol has been presented to measure the performance of instrumented treadmills and assess their accuracy [5]. However,
∗
Corresponding author. Tel.: +31 20 444 0756. E-mail addresses: [email protected], [email protected] (L.H. Sloot), [email protected] (H. Houdijk), [email protected] (M.M. van der Krogt), [email protected] (J. Harlaar).
it is also imperative to improve their accuracy through optimal calibration procedures. On site calibration procedures have been developed for conventional force plates that match recorded GRFs and COP against reference measurements. These reference values can be established in several ways; by using static weights [8], an instrumented pole [9–13], an (automated) platform testing rig with a loading rod [14–18], or a dynamic construction, such as a cylindrical container with a rotating mass [19], a 3D pendulum construction [20] or an artificial leg [21]. Most of these calibration methods require sophisticated set-ups around the force plate and are therefore impractical to use on a large treadmill, except for the weights and instrumented pole. Static weights have been used for calibration of instrumented treadmills, however, they are impractical for the calibration of horizontal forces. An instrumented pole facilitates the application of varying forces in different directions within a single measurement and has been shown to result in higher accuracy compared with weights [13]. For this type of calibration, an easy to perform protocol has been published by Collins and colleagues that describes how to capture data and calculate the calibration matrix [13]. The protocol consists of trials of 5s at 20 spots distributed over the treadmill belt. However, the chosen number of spots and measurement time are not substantiated, and accuracy might be further improved by
http://dx.doi.org/10.1016/j.medengphy.2016.04.012 1350-4533/© 2016 IPEM. Published by Elsevier Ltd. All rights reserved.
Please cite this article as: L.H. Sloot et al., Optimal calibration of instrumented treadmills using an instrumented pole, Medical Engineering and Physics (2016), http://dx.doi.org/10.1016/j.medengphy.2016.04.012
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Fig. 1. The instrumented calibrator (left), setup of the measurement (middle) and the distribution of measurement spots on the treadmill (right). The latter includes the total calibration (red circles), standard calibration (blue cross) and validation (green triangles) measurements. In addition, the COP measured during a few minutes of treadmill walking is given in black stars. The filled circles and triangles are the selected measurements used for the calibration within the walking area. The relative large distance to the edge of the belt that is not calibrated is due to the size of the metal plate used to rest the tip of the calibrator upon. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
increasing them; or the same accuracy might be obtained from fewer measurements. In addition, correction for possible nonlinearity resulting, for instance, from asymmetrical distortion moments on the force sensors by bending of the plates might further increase the accuracy [8,22]. In this study we examined if this calibration protocol using an instrumented pole can be optimized by: 1. finding the optimal measurement duration and number of spots; 2. accounting for nonlinearity in the calibration matrix; 3. accounting for inhomogeneity in the distribution of errors across the belt surface. In addition, the repeatability of the standard calibration procedure was determined. 2. Methods 2.1. Protocol The principle of the calibration procedure was based on the protocol previously outlined by Collins et al. [13]. The force and COP measurements were calibrated by maximizing the match between treadmill output and reference data measured with an instrumented pole on a stationary treadmill. An instrumented calibrator (1.12 m, 5.3 kg) was used (Fig. 1), equipped with four optical markers and a 1 DOF axial load cell (S-type, Revere Transducers Europe) mounted within its frame (Motekforce Link, Netherlands). To limit forces that are not applied along the central axis, a compliant joint system was used on the inside of the calibrator to redistribute these forces to the central axis. A metal loading plate with a shallow hole was used to increase accuracy by applying a distributed load [23]. The tip of the calibrator was minimized
with optimized friction to the metal plate and forces were exerted by pulling a handle attached to the calibrator with a rope. This instrumented calibrator gave comparable calibration results as a conventional instrumented pole (see Supplementary material). To determine the COP and the orientation of the calibrator, the lower tip was identified as a virtual marker by establishing its position relative to three of the technical markers using functional calibration, defining the tip as the position the calibrator was circled around on the treadmill belt in a calibration trial [24]. A dataset of 55 spots of 5s each was measured to construct different calibration matrices (Fig. 1). A selection of 20 spots uniformly spread over the area of each belt constituted the standard calibration dataset. Also, a validation dataset of 11 measurements per belt was collected to determine the accuracy of the calibration matrices. The following day, another standard calibration and validation dataset were collected. During the measurements, a force was applied through the calibrator by initially exerting as much vertical load as possible on the treadmill, followed by a slowly circular movement, applying as much load as possible in the horizontal directions. The instrumented dual belt treadmill (50 × 200 cm/belt, R-Mill, Motekforce Link, Netherlands) had six force sensors under each belt with a full scale output of 10 0 0 N in the horizontal and 10,0 0 0 N in the vertical direction [5]. To demonstrate the effect of the calibrations on gait data, force data were measured while a single subject (F, 28 year, 70 kg) walked on the treadmill at 3 km/h. Approval of the local ethics committee and written consent was provided. 2.2. Data analysis Treadmill, load cell (both sampled at 10 0 0 Hz), and motion (100 Hz) data were synchronized, down sampled to 100 Hz and
Please cite this article as: L.H. Sloot et al., Optimal calibration of instrumented treadmills using an instrumented pole, Medical Engineering and Physics (2016), http://dx.doi.org/10.1016/j.medengphy.2016.04.012
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low pass filtered with a 3rd-order Butterworth filter with a cutoff frequency of 5 Hz to reduce noise effects. The reference data were processed as follows. The virtual marker was used to track the point of force application as well as the orientation of the calibrator using the upper markers. The orientation was subsequently used to decompose the measured 1D force into 3D forces along the three orthogonal axes of the global treadmill coordinate system [13]. The load cell of the calibrator was calibrated by applying weights of 30, 15 and 0 kg on the calibrator while it was positioned vertically using a level and measuring an offset trial with the calibrator lying horizontally. A calibration matrix C (12 × 12; 6 × 6 matrix per belt and their crosstalk) was constructed by minimizing the mean least squares error between the reference 3D forces and 3D moments per belt measured by the calibrator in matrix R [12xtime], and the 12 treadmill sensor outputs in volts in matrix STM(V) [12xtime], with the unloaded offset (Offset(V) ) subtracted, as described by Collins et al. [13]:
C = R/(STM(V) − Offset(V) )
(1)
This matrix C gives the transformation from the output of the 12 treadmill sensors in volts (STM(V) ) to three orthogonal forces in newtons and moments in newton meters (STM(N) ) per belt by:
STM(N) = (STM(V) − Offset(V) ) ∗ C
(2)
The COP (relative to the mechanical zero) was subsequently calculated as follows:
COPml =
Fml × COPvert − Map Fvert
COPap =
3
2.4. Accounting for nonlinear terms A local matrix was calculated per belt, thus ignoring crosstalk between plates in contrast to the standard approach. In addition, matrices were constructed including offset and different nonlinear terms:
C = R/[S0 ; S1 ; S2 ; S3 ; S4 ]
(4)
with C the calibration matrix describing the transformation between a matrix containing the treadmill sensor output (S1 ) as well as higher orders of these output (S2 ,…) and offset terms (S0 ) to forces and moments. 2.5. Spatial correction After the standard calibration of the treadmill output, there can be an unequal distribution of COP error over the belt surface. To reduce this error within the primary walking area, a simple approach was first evaluated in which only the measurement spots within this area were included in the calibration dataset (Fig. 1). In addition, spatial nonlinearity over the whole belt surface was taken into account by more advanced post hoc spatial correction. The full calibration dataset (55 measurement spots) was used to determine correction coefficients based on two methods described in literature for ground mounted force plates. The first method was proposed by Schmiedmayer et al. (referred to as method S) [25]:
COPx = ( p1x + p2x COP2y + p3x COP4y )COPx + ( p4x + p5x COP2y
Fap × COPvert + Mml Fvert
+ p6x COP4y )COP3x
(3) with F is the force, M is the moment, ap is anterior-posterior, ml is medio-lateral, vert is the vertical direction, and COPvert is the vertical distance between exerted force and the treadmill sensors. The calibration dataset was used to construct calibration matrices according to Eq. (1), the accuracy of which was tested on the validation dataset using Eq. (2). The forces and COP calculated from the treadmill output were compared with the reference forces and COP calculated from the calibrator. The accuracy was calculated as the root mean square error (RMSE) between treadmill and reference data per measurement spot, and the total error was reported as the mean RMSE over spots as well as the resultant over the mean per directions. To illustrate the effect of the different calibration approaches on gait data, the COP was calculated for a left and right step on the treadmill using the standard calibration as well as other methods.
(5)
and the second method by Verkerke et al. (method V) [8]:
COPx = p1x + p2x COPx + p3x COP2x + p4x COP3x + p5x COPy
(6)
with COPx the difference between the COP calculated from the calibrated treadmill data using the standard calibration matrix and the calibrator, p1 X , … the error map correction coefficients for the x-axis, and COPy , COPx the calibrated treadmill force data. The correction coefficients for the y-axis were determined similarly. Once the correction coefficients were estimated from the calibration dataset, the final accuracy of COPx and COPy were calculated from the validation set:
COPfinal,x = COPx − COPx ;
COPfinal,y = COPy − COPy
(7)
with COPfinal the COP after spatial correction. To determine the effect of this correction, it was applied to the validation dataset after standard calibration.
2.3. Measurement duration and number of spots 2.6. Repeatability To examine if shorter measurements might be sufficient, an incremental part of the data was selected per measurement spot, from 0.5s up to the full 5s. The effect of the number of spots on the construction of the calibration matrix was examined by varying the selected number between 4 and 55 spots. To reduce the influence of a specific measurement, a selective bootstrapping method of 50 repetitions was used for each number of spots, in which combinations of spots were randomly drawn, stratified by the front, middle and back sections of the treadmill to warrant global spread. For each combination of duration and subset of measurement spots, a new calibration matrix was constructed. The accuracies were based on the same validation dataset. The average error (over repetitions) as a function of number of spots was smoothed (moving average filter with a span of 4 spots). The optimal number of spots was defined as the number at which the decrease in error reached below 1%, and the optimal duration was taken as the duration with the lowest error. This optimal combination is referred to as the standard+ calibration.
Repeated measurements were taken to create a context to interpret the effect of different calibration approaches. A standard calibration dataset (20 spots per belt) and validation dataset were captured on two consecutive days. To determine the between-day repeatability of the entire procedure, a new matrix was calculated using the calibration set of day 2 and the accuracy determined using the validation set of day 2. To determine the effect of the calibration data on the calculated matrix, the accuracy of the calibration matrices of both days were compared using the validation dataset of day 1. 3. Results 3.1. Measurement duration and number of spots Generally, the accuracy of force and COP increased with increasing duration and number of spots (Fig. 3). For the left belt, the
Please cite this article as: L.H. Sloot et al., Optimal calibration of instrumented treadmills using an instrumented pole, Medical Engineering and Physics (2016), http://dx.doi.org/10.1016/j.medengphy.2016.04.012
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Table 1 Accuracy of different calibration methods. Calibration method
Average RMSE per directions F(N)
Trial length and number of spots Standard calibration 20 spots, 5s
Resultant RMSE COP (mm)
2.09 ± 0.50 2.46 ± 0.96 4.25 ± 1.22 2.16 ± 0.52
ml: ap:
Standard+ calibration
ml: ap: vert: ml:
30 spots, 5s
ap:
2.55 ± 0.99
ml: ap: vert: ml: ap: vert: ml: ap: vert: ml: ap: vert: ml: ap: vert: ml: ap: vert:
2.08 ± 0.50 2.45 ± 0.96 4.25 ± 1.22 2.11 ± 0.54 2.36 ± 0.90 2.84 ± 1.38 2.09 ± 0.52 2.48 ± 1.03 3.83 ± 1.16 2.10 ± 0.53 2.42 ± 1.01 2.70 ± 0.96 2.11 ± 0.58 2.45 ± 1.00 3.36 ± 0.80 2.11 ± 0.59 2.42 ± 1.01 2.41 ± 0.65
ml: ap: vert:
2.00 ± 0.59 2.68 ± 1.10 4.44 ± 1.66
Non-linear terms Local calibration 20 spots, 5s Offset 20 spots, 5s Non-linear: x+x2 20 spots, 5s Non-linear: x+x2 +offset 20 spots, 5s Non-linear: x+x2 +x3 20 spots, 5s Non-linear: x+x2 +x3 +offset 20 spots, 5s Spatial correction Walking area 16 spots, 5s Schmiedmayer 55 spots, 5s Verkerke 55 spots, 5s
F (N)
COP (mm)
2.09 ± 2.74 4.17 ± 3.71
res:
5.34
res:
ml:
2.01 ± 2.41
res:
5.40
res:
4.24
ap:
3.73 ± 3.54
࢞:
0.06
࢞:
−0.42
ml: ap:
2.09 ± 2.74 4.17 ± 3.71
res: ࢞:
5.33 −0.01
res: ࢞:
4.66 0.00
ml: ap:
2.88 ± 3.27 7.24 ± 5.94
res: ࢞:
4.26 −1.08
res: ࢞:
7.80 3.14
ml: ap:
2.00 ± 1.95 4.29 ± 3.05
res: ࢞:
5.02 −0.32
res: ࢞:
4.73 0.08
ml: ap:
2.15 ± 2.11 6.08 ± 4.60
res: ࢞:
4.19 −1.15
res: ࢞:
6.45 1.79
ml: ap:
1.91 ± 1.78 5.07 ± 4.56
res: ࢞:
4.67 −0.67
res: ࢞:
5.42 0.76
ml: ap:
2.22 ± 1.91 7.33 ± 6.42
res: ࢞:
4.01 −1.33
res: ࢞:
7.66 3.00
ml: ap:
2.16 ± 2.04 3.87 ± 3.30
res: ࢞:
5.56 0.22
res: ࢞:
4.43 −0.23
ml: ap: ml: ap:
2.19 ± 2.44 4.46 ± 3.14 2.34 ± 2.90 3.96 ± 3.86
res: ࢞: res: ࢞:
4.96 0.30 4.60 −0.06
4.66
Effect of different calibration approaches on the force and COP accuracy calculated from the same validation dataset. With F, force; COP, center of pressure; ml, mediolateral; ap, anterior-posterior; vert, vertical direction; and ࢞, the difference with the standard calibration (negative value is lower error). Per spot, the RMSE is calculated between the treadmill and calibrator data. Here, the mean RMSE and standard deviation over spots are given for the different force and COP directions, as well as the force and COP resultant (vector sum) total error (indicated as res). The numbers of spots and samples are a description of the calibration dataset used to calculate the calibration matrix for the mentioned approach.
optimal calibration data set constituted 15–30 and 27 spots when considering the different directions for force and COP error respectively, with a duration of 4–5s. For the right belt, a number of 8–9 and 15–26 spots were optimal, with a duration varying between 2–4s and 2–5s. Hence, in order to fulfill our criterion for all parameters, the standard+ calibration consisted of 30 spots of 5s each, resulting in a comparable (0.06 N higher) resultant force error and a 0.42 mm lower COP error compared with standard calibration (Table 1). Standard+ gave similar COP during gait as the standard calibration (Fig. 2).
3.3. Spatial correction There was an unequal distribution of COP error over the belt surface after standard calibration (Fig. 4). Although calibration focused on the primary walking area resulted in similar overall accuracy as the standard calibration (Table 1), validation within the walking area showed a significant local decrease of 1.62 mm (Table 2), which is represented by the reduction within the walking area in Fig. 4. This figure also shows that the spatial correction algorithms resulted in a more equal distribution of the COP error, from a range of 19.0–17.3 mm with standard calibration, to 1.3–14.6 and 2.2–7.5 mm for method S and V, respectively. Both methods did not decrease in resultant COP error (Table 1) compared with standard calibration, however, especially method V reached a lower COP error in the walking area (Table 2).
3.2. Accounting for nonlinear terms 3.4. Repeatability The simple local calibration matrix, without crosstalk between belts, resulted in comparable resultant force and COP errors as the standard calibration (Table 1). Inclusion of offset terms resulted in slightly lower resultant force errors compared with standard calibration (1.08–1.33 N for the different nonlinear terms), but higher COP errors (1.79–3.14 mm). Similar results were found with the inclusion of higher order terms, but with slightly increased COP error (0.08–0.76 mm). Inclusion of the second order term resulted in relatively large deviations from the COP during gait as calculated with the standard calibration (Fig. 2).
Between days differences for the whole calibration and validation procedure, i.e. C1 + V1 vs. C2 + V2, were 2.14 N and 0.36 mm (Table 3). Differences between calibration matrices, i.e. C1 + V1 vs. C2 + V1, were 6.30 N and 0.54 mm. 4. Discussion In this study we examined if the standard calibration protocol using an instrumented pole can be further optimized for
Please cite this article as: L.H. Sloot et al., Optimal calibration of instrumented treadmills using an instrumented pole, Medical Engineering and Physics (2016), http://dx.doi.org/10.1016/j.medengphy.2016.04.012
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Fig. 2. Effect of different calibration matrices (different colors) on the COP of a single step, one left (upper figure) and one right stride (lower figure). The Verkerke method was used to illustrate the effect of spatial correction. Table 2 Effect of spatial correction on accuracy of walking area. Calibration method
Average RMSE per direction F(N)
Standard calibration
Standard+ calibration
Walking area
Schmiedmayer Verkerke
ml: ap: vert: ml: ap: vert: ml: ap: vert:
Resultant RMSE COP (mm)
2.14 ± 0.65 2.26 ± 0.72 3.94 ± 1.02 2.17 ± 0.68 2.37 ± 0.68 3.74 ± 1.07 2.08 ± 0.70 2.36 ± 0.71 3.61 ± 0.86
F (N)
COP (mm)
ml: ap:
3.70 ± 4.13 5.17 ± 5.08
res:
5.02
res:
6.36
ml: ap:
3.28 ± 3.52 4.51 ± 4.48
res: ࢞:
4.93 −0.09
res: ࢞:
5.58 −0.78
ml: ap:
2.66 ± 2.88 3.92 ± 3.81
res: ࢞:
4.79 −0.23
res: ࢞:
4.74 −1.62
ml: ap: ml: ap:
3.32 ± 3.76 5.04 ± 3.92 3.89 ± 4.22 4.15 ± 4.04
res: ࢞: res: ࢞:
6.04 −0.32 5.69 −0.67
Effect of selected calibration approaches on the force and COP accuracy of the trials of the validation dataset in the walking area (see Fig. 1). With F, force; COP, center of pressure; ml, mediolateral; ap, anterior-posterior; vert, vertical direction; res, the resultant error; and ࢞, the difference with the standard calibration (negative value representing a lower error).
instrumented treadmills [13]. First, we examined whether the applicability of the protocol could be improved by including fewer or shorter measurements while reaching the same accuracy, or whether the accuracy improved by increasing the number of spots. The addition of extra spots was found to increase the COP accuracy compared with the 20 spots used by Collins et al. [13], while a reduction negatively affected the accuracy. In addition, accuracy generally decreased with a reduction of measurement duration, most prominently for left belt COP and right belt COPml , but not for all directions. For instance, the first part of the data contained the largest range and highest magnitude of vertical forces, so for this direction the accuracy did not improve with a longer duration. It was not examined whether increasing the measurement time would further increase the accuracy, however, the maximum measurement time (5s) seemed sufficient to exert a wide range of forces as the error leveled off, while at a longer duration fatigue is expected to negatively affect the exertion of high loads. The
optimal calibration dataset for all directions consisted of 30 spots per belt of 5s each, and improved the COP accuracy. Different approaches to construct the calibration matrix were examined. The local calibration reached the same accuracy as the standard calibration, indicating that crosstalk between the belts did not largely affect the force and COP accuracy. This is in agreement with the small crosstalk of below 1.5% measured for this treadmill [5]. Inclusion of offset and nonlinear terms slightly improved force accuracy, but negatively affected COP accuracy, which is in agreement with a previous study that found no accuracy improvement after addition of nonlinear terms [13]. After standard calibration, an inhomogeneous distribution of the COP error was found across the surface of the treadmill. These spatial differences could not have resulted from the specific order of the measurements or fatigue of the investigator applying the forces, because similar results were found in additional measurements the following day, while measuring in a different order
Please cite this article as: L.H. Sloot et al., Optimal calibration of instrumented treadmills using an instrumented pole, Medical Engineering and Physics (2016), http://dx.doi.org/10.1016/j.medengphy.2016.04.012
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Fig. 3. The effect of number of measurement spots and number of data samples on the resultant COP and force errors for the left and right belt (with blue indicating lower and red higher errors). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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Fig. 4. Spatial distribution of the RMSE COP for different calibration methods. The methods are without COP correction (A), with COP correction based on the method described by Schmiedmayer (B), or by Verkerke (C) and using the calibration matrix focused on the walking area (D). Indicated are the resultant (over anterior-posterior and medio-lateral direction) errors between treadmill and instrumented calibrator measurements (with green indicating lower and yellow higher errors). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) Table 3 Repeatability. Calibration method
Average RMSE per direction Day 1
Between day C1+V1 vs. C2+V2
Calibration data C1+V1 vs. C2+V1
F (N): ml: ap: vert: COP (mm): ml: ap: F (N): ml: ap: vert: COP (mm): ml:
Difference between days
Day 2
2.09 ± 0.50 2.46 ± 0.96 4.25 ± 1.22
2.53 ± 1.104 3.27 ± 1.49 6.18 ± 1.65
0.44 0.81 1.93
Fres (N):
2.14
2.09 ± 2.74 4.17 ± 3.71
1.73 ± 1.28 4.12 ± 2.15
0.36 0.05
COPres (mm):
0.36
2.09 ± 0.50 2.46 ± 0.96 4.25 ± 1.22
2.81 ± 0.96 2.15 ± 0.80 10.50 ± 3.49
0.72 0.31 6.25
Fres (N):
6.30
2.09 ± 2.74
2.63 ± 1.83
0.54
COPres (mm):
0.54
C1 refers to the calibration data set captured at day 1 that was used to calculate the calibration matrix and V1 the validation set captured at day 1 used to calculate the calibration matrix accuracy. Similarly, C2 and V2 refer to the calibration data and validation data captured at day 2. With F, force in N; COP, center of pressure in mm; res, resultant error; ml, mediolateral; ap, anterior-posterior; and vert, vertical direction.
(Supplementary material). It could have been caused by slight bending of the large force plates, which is less of a problem in ground mounted force plates. Still, error distributions have also been reported for these conventional force plates, with lowest errors in the center region [14,15]. Since the errors were not optimal within the walking area for our treadmill, the accuracy could be locally improved. A simple approach was to include only data from within this area, showing a significant increase in local COP accuracy that was larger than the variability measured between days. This could potentially be further increased by using a smaller metal plate which limited the distance to the belt edge. Alternatively, the nonlinearity in COP error could be reduced across the whole belt by correcting for the positional dependence. The method of Verkerke et al. [8] showed the best improvement across the belt surface (Fig. 4) and reduction within the walking
area. This could be interesting when subjects are not expected to limit their gait to a central area of the treadmill, for instance due to destabilizing perturbations. The optimization of the calibration methods using an instrumented calibrator only seemed to improve the overall accuracy to a limited extent, suggesting the maximal accuracy of this treadmill is approached given its inherent mechanical limitations. The accuracy reached after the different calibrations was within the range reported for most treadmills [13,26–28], although better (errors of 1.2–1.7 mm [29,30]) and worse (20–40 mm [8,31]) COP accuracies have also been reported. The differences between the various calibration methods in the calculated COP during gait (Fig. 2) were relatively small, with the largest difference around 5 mm for the medio-lateral direction on the left belt. Even so, average errors of around 2 and 4 mm in the different directions
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remained, although part of the error might be random and can be averaged away over multiple strides. It has been shown that shifts of 10 mm in the anterior-posterior COP can considerably alter the magnitude of joint kinetics, up to a 7% change in the ankle flexion moment, and 16% in knee and 8% in hip flexion moment [1,4,32]. A similar shift in the medio-lateral direction has been shown to reverse the pattern of ankle joint inversion-eversion moment [32]. This emphasizes the importance of calibration and, although the optimal calibration might depend on the treadmill and required accuracy for a measurement, this study provides several pointers to optimize the calibration protocol for a given instrumented treadmill. Future steps should not only focus on improvement of treadmill constructions, but also on decreasing the variability between calibration sessions to ensure an optimal and stable level of accuracy for a gait lab. This repeatability could benefit from further standardization of the calibration protocol, for instance by predefining a grid for the measurement spots and providing feedback on the exerted force to ensure a representative range of forces is included. In addition, the design of the instrumented pole could be improved, to enable exertion of representative forces and increase user friendliness, including limiting preparation time and designing an ergonomic grip. Furthermore, it would be interesting for quality assurance to examine the accuracy of a calibration matrix over time, by capturing different validation sets over a longer period of time. Lastly, the question remains whether static calibration provides the best transformation matrix for the treadmill outputs under experimental conditions, i.e. with a running belt. Future research should compare the accuracy of static with dynamic calibration techniques under these experimental conditions. Thus, the optimal calibration dataset consisted of 30 measurements per belt of 5s each. In addition, both correction for position dependence of COP error as well as its optimization within the walking area are found to be valuable additions to the standard calibration process. Potential improvements that should be further examined include standardization of force application, improvement of pole design, and applicability under experimental conditions. Conflict of interest The authors have no conflict of interest. Acknowledgments The authors would like to thank Bert Clairbois, Josien van den Noort, Adam Rozumalski, Pedro De Jesus Pereira Custódio and Linda van Gelder for their technical or measurement assistance. This study was financially supported by the Dutch Technology Foundation STW (#10733). None of the authors have competing interests. Ethical approval was provided by the local ethical committee of the Human Movement Faculty of the VU University. Supplementary materials Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.medengphy.2016.04. 012. References
[2] Riemer R, Hsiao-Wecksler ET, Zhang XD. Uncertainties in inverse dynamics solutions: a comprehensive analysis and an application to gait. Gait Posture 2008;27:578–88. [3] Silva MPT, Ambrosio JAC. Sensitivity of the results produced by the inverse dynamic analysis of a human stride to perturbed input data. Gait Posture 2004;19:35–49. [4] McCaw ST, DeVita P. Errors in alignment of center of pressure and foot coordinates affect predicted lower extremity torques. J Biomech 1995;28:985–8. [5] Sloot L, Houdijk H, Harlaar J. A comprehensive protocol to test instrumented treadmills. J Med Eng Phys 2015;37:610–16. [6] van den Noort JC, Steenbrink F, Roeles S, Harlaar J. Real-time visual feedback for gait retraining: toward application in knee osteoarthritis. Med Biol Eng Comput 2015;53:275–86. [7] Rouse EJ, Hargrove LJ, Perreault EJ, Peshkin MA, Kuiken TA. Development of a mechatronic platform and validation of methods for estimating ankle stiffness during the stance phase of walking. 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Gait Posture 2009;29:59–64. [14] Hsieh HJ, Lu TW, Chen SC, Chang CM, Hung CH. A new device for in situ static and dynamic calibration of force platforms. Gait Posture 2011;33:701–5. [15] Dias JA, Dal Pupo J, Reis DC, Borges L, Santos SG, Moro ARP, et al. Validity of two methods for estimation of vertical jump height. J Strength Cond Res 2011;25:2034–9. [16] Chockalingam N, Giakas G, Iossifidou A. Do strain gauge force platforms need in situ correction? Gait Posture 2002;16:233–7. [17] Gill HS, OConnor JJ. A new testing rig for force platform calibration and accuracy tests. Gait Posture 1997;5:228–32. [18] Hall MG, Fleming HE, Dolan MJ, Millbank SFD, Paul JP. Static in situ calibration of force plates. J Biomech 1996;29:659–65. [19] Morasso PG, Re C, Casadio M. Spot check and recalibration of stabilometric platforms. Technol Health Care 2004;12:293–304. [20] Fairburn PS, Palmer R, Whybrow J, Fielden S, Jones S. A prototype system for testing force platform dynamic performance. 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Am J Phys Med Rehabil 2008;87:515–26. [27] Kram R, Griffin TM, Donelan JM, Chang YH. Force treadmill for measuring vertical and horizontal ground reaction forces. J Appl Physiol 1998;85:764–9. [28] Paolini G, Della Croce U, Riley PO, Newton FK, Kerrigan DC. Testing of a tri-instrumented-treadmill unit for kinetic analysis of locomotion tasks in static and dynamic loading conditions. Med Eng Phys 2007;29:404–11. [29] Goldberg SR, Kepple TM, Stanhope SJ. In situ calibration and motion capture transformation optimization improve instrumented treadmill measurements. J Appl Biomech 2009;25:401–6. [30] Luciani LB, Genovese V, Monaco V, Odetti L, Cattin E, Micera S. Design and Evaluation of a new mechatronic platform for assessment and prevention of fall risks. J Neuroeng Rehabil 2012;9(1):1–13. [31] Bagesteiro LB, Gould D, Ewins DJ. A vertical ground reaction force-measuring treadmill for the analysis of prosthetic limbs. Braz J Biomed Eng 2011;27:3–77. [32] Kim H, Sakurai S, Ahn J. 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[1] Pamies-Vila R, Font-Llagunes JM, Cuadrado J, Alonso FJ. Analysis of different uncertainties in the inverse dynamic analysis of human gait. Mech Mach Theory 2012;58:153–64.
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Technical note
Optimal calibration of instrumented treadmills using an instrumented pole L.H. Sloot a,b,∗, H. Houdijk b,c, M.M. van der Krogt a,b, J. Harlaar a,b a
VU University Medical Center, Department of Rehabilitation Medicine, PO Box 7057, 1007 MB Amsterdam, The Netherlands Research Institute MOVE, VU University Amsterdam, Van der Boechorststraat 7, 1081 BT Amsterdam, The Netherlands c Heliomare Rehabilitation Center, Research and Development, Relweg 51, 1949 EC Wijk aan Zee, The Netherlands b
a r t i c l e
i n f o
Article history: Received 9 September 2015 Revised 14 March 2016 Accepted 11 April 2016 Available online xxx Keywords: Kinematics Biomechanics Center of pressure Kinetics Gait analysis
a b s t r a c t Calibration of instrumented treadmills is imperative for accurate measurement of ground reaction forces and center of pressure (COP). A protocol using an instrumented pole has been shown to considerably increase force and COP accuracy. This study examined how this protocol can be further optimized to maximize accuracy, by varying the measurement time and number of spots, using nonlinear approaches to calculate the calibration matrix and by correcting for potential inhomogeneity in the distribution of COP errors across the treadmill’s surface. The accuracy increased with addition of spots and correction for the inhomogeneous distribution across the belt surface, decreased with reduction of measurement time, and did not improve by including nonlinear terms. Most of these methods improved the overall accuracy only to a limited extent, suggesting that the maximal accuracy is approached given the treadmill’s inherent mechanical limitations. However, both correction for position dependence of the accuracy as well as its optimization within the walking area are found to be valuable additions to the standard calibration process. © 2016 IPEM. Published by Elsevier Ltd. All rights reserved.
1. Introduction In gait analysis, normal and pathological gait patterns are examined on the basis of joint kinematics and kinetics. The latter includes net joint moments and powers, which are calculated through inverse dynamics using a linked segment model with mass distribution, kinematics, ground reaction forces (GRF) and moments, as well as hereof derived center of pressure (COP). Of all these data, errors in GRF and thus COP have been shown to be the main source of inaccuracies in lower body kinetics [1–4]. These errors are generally larger in instrumented treadmills compared with conventional force plates that are incorporated in the floor, because of their large and compliant structure [5]. Moreover, novel applications of these treadmills, such as feedback on frontal knee moments during gait [6] or system identification of the neuromuscular system [7], require highly accurate force measurements. Recently, a protocol has been presented to measure the performance of instrumented treadmills and assess their accuracy [5]. However,
∗
Corresponding author. Tel.: +31 20 444 0756. E-mail addresses: [email protected], [email protected] (L.H. Sloot), [email protected] (H. Houdijk), [email protected] (M.M. van der Krogt), [email protected] (J. Harlaar).
it is also imperative to improve their accuracy through optimal calibration procedures. On site calibration procedures have been developed for conventional force plates that match recorded GRFs and COP against reference measurements. These reference values can be established in several ways; by using static weights [8], an instrumented pole [9–13], an (automated) platform testing rig with a loading rod [14–18], or a dynamic construction, such as a cylindrical container with a rotating mass [19], a 3D pendulum construction [20] or an artificial leg [21]. Most of these calibration methods require sophisticated set-ups around the force plate and are therefore impractical to use on a large treadmill, except for the weights and instrumented pole. Static weights have been used for calibration of instrumented treadmills, however, they are impractical for the calibration of horizontal forces. An instrumented pole facilitates the application of varying forces in different directions within a single measurement and has been shown to result in higher accuracy compared with weights [13]. For this type of calibration, an easy to perform protocol has been published by Collins and colleagues that describes how to capture data and calculate the calibration matrix [13]. The protocol consists of trials of 5s at 20 spots distributed over the treadmill belt. However, the chosen number of spots and measurement time are not substantiated, and accuracy might be further improved by
http://dx.doi.org/10.1016/j.medengphy.2016.04.012 1350-4533/© 2016 IPEM. Published by Elsevier Ltd. All rights reserved.
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Fig. 1. The instrumented calibrator (left), setup of the measurement (middle) and the distribution of measurement spots on the treadmill (right). The latter includes the total calibration (red circles), standard calibration (blue cross) and validation (green triangles) measurements. In addition, the COP measured during a few minutes of treadmill walking is given in black stars. The filled circles and triangles are the selected measurements used for the calibration within the walking area. The relative large distance to the edge of the belt that is not calibrated is due to the size of the metal plate used to rest the tip of the calibrator upon. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
increasing them; or the same accuracy might be obtained from fewer measurements. In addition, correction for possible nonlinearity resulting, for instance, from asymmetrical distortion moments on the force sensors by bending of the plates might further increase the accuracy [8,22]. In this study we examined if this calibration protocol using an instrumented pole can be optimized by: 1. finding the optimal measurement duration and number of spots; 2. accounting for nonlinearity in the calibration matrix; 3. accounting for inhomogeneity in the distribution of errors across the belt surface. In addition, the repeatability of the standard calibration procedure was determined. 2. Methods 2.1. Protocol The principle of the calibration procedure was based on the protocol previously outlined by Collins et al. [13]. The force and COP measurements were calibrated by maximizing the match between treadmill output and reference data measured with an instrumented pole on a stationary treadmill. An instrumented calibrator (1.12 m, 5.3 kg) was used (Fig. 1), equipped with four optical markers and a 1 DOF axial load cell (S-type, Revere Transducers Europe) mounted within its frame (Motekforce Link, Netherlands). To limit forces that are not applied along the central axis, a compliant joint system was used on the inside of the calibrator to redistribute these forces to the central axis. A metal loading plate with a shallow hole was used to increase accuracy by applying a distributed load [23]. The tip of the calibrator was minimized
with optimized friction to the metal plate and forces were exerted by pulling a handle attached to the calibrator with a rope. This instrumented calibrator gave comparable calibration results as a conventional instrumented pole (see Supplementary material). To determine the COP and the orientation of the calibrator, the lower tip was identified as a virtual marker by establishing its position relative to three of the technical markers using functional calibration, defining the tip as the position the calibrator was circled around on the treadmill belt in a calibration trial [24]. A dataset of 55 spots of 5s each was measured to construct different calibration matrices (Fig. 1). A selection of 20 spots uniformly spread over the area of each belt constituted the standard calibration dataset. Also, a validation dataset of 11 measurements per belt was collected to determine the accuracy of the calibration matrices. The following day, another standard calibration and validation dataset were collected. During the measurements, a force was applied through the calibrator by initially exerting as much vertical load as possible on the treadmill, followed by a slowly circular movement, applying as much load as possible in the horizontal directions. The instrumented dual belt treadmill (50 × 200 cm/belt, R-Mill, Motekforce Link, Netherlands) had six force sensors under each belt with a full scale output of 10 0 0 N in the horizontal and 10,0 0 0 N in the vertical direction [5]. To demonstrate the effect of the calibrations on gait data, force data were measured while a single subject (F, 28 year, 70 kg) walked on the treadmill at 3 km/h. Approval of the local ethics committee and written consent was provided. 2.2. Data analysis Treadmill, load cell (both sampled at 10 0 0 Hz), and motion (100 Hz) data were synchronized, down sampled to 100 Hz and
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low pass filtered with a 3rd-order Butterworth filter with a cutoff frequency of 5 Hz to reduce noise effects. The reference data were processed as follows. The virtual marker was used to track the point of force application as well as the orientation of the calibrator using the upper markers. The orientation was subsequently used to decompose the measured 1D force into 3D forces along the three orthogonal axes of the global treadmill coordinate system [13]. The load cell of the calibrator was calibrated by applying weights of 30, 15 and 0 kg on the calibrator while it was positioned vertically using a level and measuring an offset trial with the calibrator lying horizontally. A calibration matrix C (12 × 12; 6 × 6 matrix per belt and their crosstalk) was constructed by minimizing the mean least squares error between the reference 3D forces and 3D moments per belt measured by the calibrator in matrix R [12xtime], and the 12 treadmill sensor outputs in volts in matrix STM(V) [12xtime], with the unloaded offset (Offset(V) ) subtracted, as described by Collins et al. [13]:
C = R/(STM(V) − Offset(V) )
(1)
This matrix C gives the transformation from the output of the 12 treadmill sensors in volts (STM(V) ) to three orthogonal forces in newtons and moments in newton meters (STM(N) ) per belt by:
STM(N) = (STM(V) − Offset(V) ) ∗ C
(2)
The COP (relative to the mechanical zero) was subsequently calculated as follows:
COPml =
Fml × COPvert − Map Fvert
COPap =
3
2.4. Accounting for nonlinear terms A local matrix was calculated per belt, thus ignoring crosstalk between plates in contrast to the standard approach. In addition, matrices were constructed including offset and different nonlinear terms:
C = R/[S0 ; S1 ; S2 ; S3 ; S4 ]
(4)
with C the calibration matrix describing the transformation between a matrix containing the treadmill sensor output (S1 ) as well as higher orders of these output (S2 ,…) and offset terms (S0 ) to forces and moments. 2.5. Spatial correction After the standard calibration of the treadmill output, there can be an unequal distribution of COP error over the belt surface. To reduce this error within the primary walking area, a simple approach was first evaluated in which only the measurement spots within this area were included in the calibration dataset (Fig. 1). In addition, spatial nonlinearity over the whole belt surface was taken into account by more advanced post hoc spatial correction. The full calibration dataset (55 measurement spots) was used to determine correction coefficients based on two methods described in literature for ground mounted force plates. The first method was proposed by Schmiedmayer et al. (referred to as method S) [25]:
COPx = ( p1x + p2x COP2y + p3x COP4y )COPx + ( p4x + p5x COP2y
Fap × COPvert + Mml Fvert
+ p6x COP4y )COP3x
(3) with F is the force, M is the moment, ap is anterior-posterior, ml is medio-lateral, vert is the vertical direction, and COPvert is the vertical distance between exerted force and the treadmill sensors. The calibration dataset was used to construct calibration matrices according to Eq. (1), the accuracy of which was tested on the validation dataset using Eq. (2). The forces and COP calculated from the treadmill output were compared with the reference forces and COP calculated from the calibrator. The accuracy was calculated as the root mean square error (RMSE) between treadmill and reference data per measurement spot, and the total error was reported as the mean RMSE over spots as well as the resultant over the mean per directions. To illustrate the effect of the different calibration approaches on gait data, the COP was calculated for a left and right step on the treadmill using the standard calibration as well as other methods.
(5)
and the second method by Verkerke et al. (method V) [8]:
COPx = p1x + p2x COPx + p3x COP2x + p4x COP3x + p5x COPy
(6)
with COPx the difference between the COP calculated from the calibrated treadmill data using the standard calibration matrix and the calibrator, p1 X , … the error map correction coefficients for the x-axis, and COPy , COPx the calibrated treadmill force data. The correction coefficients for the y-axis were determined similarly. Once the correction coefficients were estimated from the calibration dataset, the final accuracy of COPx and COPy were calculated from the validation set:
COPfinal,x = COPx − COPx ;
COPfinal,y = COPy − COPy
(7)
with COPfinal the COP after spatial correction. To determine the effect of this correction, it was applied to the validation dataset after standard calibration.
2.3. Measurement duration and number of spots 2.6. Repeatability To examine if shorter measurements might be sufficient, an incremental part of the data was selected per measurement spot, from 0.5s up to the full 5s. The effect of the number of spots on the construction of the calibration matrix was examined by varying the selected number between 4 and 55 spots. To reduce the influence of a specific measurement, a selective bootstrapping method of 50 repetitions was used for each number of spots, in which combinations of spots were randomly drawn, stratified by the front, middle and back sections of the treadmill to warrant global spread. For each combination of duration and subset of measurement spots, a new calibration matrix was constructed. The accuracies were based on the same validation dataset. The average error (over repetitions) as a function of number of spots was smoothed (moving average filter with a span of 4 spots). The optimal number of spots was defined as the number at which the decrease in error reached below 1%, and the optimal duration was taken as the duration with the lowest error. This optimal combination is referred to as the standard+ calibration.
Repeated measurements were taken to create a context to interpret the effect of different calibration approaches. A standard calibration dataset (20 spots per belt) and validation dataset were captured on two consecutive days. To determine the between-day repeatability of the entire procedure, a new matrix was calculated using the calibration set of day 2 and the accuracy determined using the validation set of day 2. To determine the effect of the calibration data on the calculated matrix, the accuracy of the calibration matrices of both days were compared using the validation dataset of day 1. 3. Results 3.1. Measurement duration and number of spots Generally, the accuracy of force and COP increased with increasing duration and number of spots (Fig. 3). For the left belt, the
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Table 1 Accuracy of different calibration methods. Calibration method
Average RMSE per directions F(N)
Trial length and number of spots Standard calibration 20 spots, 5s
Resultant RMSE COP (mm)
2.09 ± 0.50 2.46 ± 0.96 4.25 ± 1.22 2.16 ± 0.52
ml: ap:
Standard+ calibration
ml: ap: vert: ml:
30 spots, 5s
ap:
2.55 ± 0.99
ml: ap: vert: ml: ap: vert: ml: ap: vert: ml: ap: vert: ml: ap: vert: ml: ap: vert:
2.08 ± 0.50 2.45 ± 0.96 4.25 ± 1.22 2.11 ± 0.54 2.36 ± 0.90 2.84 ± 1.38 2.09 ± 0.52 2.48 ± 1.03 3.83 ± 1.16 2.10 ± 0.53 2.42 ± 1.01 2.70 ± 0.96 2.11 ± 0.58 2.45 ± 1.00 3.36 ± 0.80 2.11 ± 0.59 2.42 ± 1.01 2.41 ± 0.65
ml: ap: vert:
2.00 ± 0.59 2.68 ± 1.10 4.44 ± 1.66
Non-linear terms Local calibration 20 spots, 5s Offset 20 spots, 5s Non-linear: x+x2 20 spots, 5s Non-linear: x+x2 +offset 20 spots, 5s Non-linear: x+x2 +x3 20 spots, 5s Non-linear: x+x2 +x3 +offset 20 spots, 5s Spatial correction Walking area 16 spots, 5s Schmiedmayer 55 spots, 5s Verkerke 55 spots, 5s
F (N)
COP (mm)
2.09 ± 2.74 4.17 ± 3.71
res:
5.34
res:
ml:
2.01 ± 2.41
res:
5.40
res:
4.24
ap:
3.73 ± 3.54
࢞:
0.06
࢞:
−0.42
ml: ap:
2.09 ± 2.74 4.17 ± 3.71
res: ࢞:
5.33 −0.01
res: ࢞:
4.66 0.00
ml: ap:
2.88 ± 3.27 7.24 ± 5.94
res: ࢞:
4.26 −1.08
res: ࢞:
7.80 3.14
ml: ap:
2.00 ± 1.95 4.29 ± 3.05
res: ࢞:
5.02 −0.32
res: ࢞:
4.73 0.08
ml: ap:
2.15 ± 2.11 6.08 ± 4.60
res: ࢞:
4.19 −1.15
res: ࢞:
6.45 1.79
ml: ap:
1.91 ± 1.78 5.07 ± 4.56
res: ࢞:
4.67 −0.67
res: ࢞:
5.42 0.76
ml: ap:
2.22 ± 1.91 7.33 ± 6.42
res: ࢞:
4.01 −1.33
res: ࢞:
7.66 3.00
ml: ap:
2.16 ± 2.04 3.87 ± 3.30
res: ࢞:
5.56 0.22
res: ࢞:
4.43 −0.23
ml: ap: ml: ap:
2.19 ± 2.44 4.46 ± 3.14 2.34 ± 2.90 3.96 ± 3.86
res: ࢞: res: ࢞:
4.96 0.30 4.60 −0.06
4.66
Effect of different calibration approaches on the force and COP accuracy calculated from the same validation dataset. With F, force; COP, center of pressure; ml, mediolateral; ap, anterior-posterior; vert, vertical direction; and ࢞, the difference with the standard calibration (negative value is lower error). Per spot, the RMSE is calculated between the treadmill and calibrator data. Here, the mean RMSE and standard deviation over spots are given for the different force and COP directions, as well as the force and COP resultant (vector sum) total error (indicated as res). The numbers of spots and samples are a description of the calibration dataset used to calculate the calibration matrix for the mentioned approach.
optimal calibration data set constituted 15–30 and 27 spots when considering the different directions for force and COP error respectively, with a duration of 4–5s. For the right belt, a number of 8–9 and 15–26 spots were optimal, with a duration varying between 2–4s and 2–5s. Hence, in order to fulfill our criterion for all parameters, the standard+ calibration consisted of 30 spots of 5s each, resulting in a comparable (0.06 N higher) resultant force error and a 0.42 mm lower COP error compared with standard calibration (Table 1). Standard+ gave similar COP during gait as the standard calibration (Fig. 2).
3.3. Spatial correction There was an unequal distribution of COP error over the belt surface after standard calibration (Fig. 4). Although calibration focused on the primary walking area resulted in similar overall accuracy as the standard calibration (Table 1), validation within the walking area showed a significant local decrease of 1.62 mm (Table 2), which is represented by the reduction within the walking area in Fig. 4. This figure also shows that the spatial correction algorithms resulted in a more equal distribution of the COP error, from a range of 19.0–17.3 mm with standard calibration, to 1.3–14.6 and 2.2–7.5 mm for method S and V, respectively. Both methods did not decrease in resultant COP error (Table 1) compared with standard calibration, however, especially method V reached a lower COP error in the walking area (Table 2).
3.2. Accounting for nonlinear terms 3.4. Repeatability The simple local calibration matrix, without crosstalk between belts, resulted in comparable resultant force and COP errors as the standard calibration (Table 1). Inclusion of offset terms resulted in slightly lower resultant force errors compared with standard calibration (1.08–1.33 N for the different nonlinear terms), but higher COP errors (1.79–3.14 mm). Similar results were found with the inclusion of higher order terms, but with slightly increased COP error (0.08–0.76 mm). Inclusion of the second order term resulted in relatively large deviations from the COP during gait as calculated with the standard calibration (Fig. 2).
Between days differences for the whole calibration and validation procedure, i.e. C1 + V1 vs. C2 + V2, were 2.14 N and 0.36 mm (Table 3). Differences between calibration matrices, i.e. C1 + V1 vs. C2 + V1, were 6.30 N and 0.54 mm. 4. Discussion In this study we examined if the standard calibration protocol using an instrumented pole can be further optimized for
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5
Fig. 2. Effect of different calibration matrices (different colors) on the COP of a single step, one left (upper figure) and one right stride (lower figure). The Verkerke method was used to illustrate the effect of spatial correction. Table 2 Effect of spatial correction on accuracy of walking area. Calibration method
Average RMSE per direction F(N)
Standard calibration
Standard+ calibration
Walking area
Schmiedmayer Verkerke
ml: ap: vert: ml: ap: vert: ml: ap: vert:
Resultant RMSE COP (mm)
2.14 ± 0.65 2.26 ± 0.72 3.94 ± 1.02 2.17 ± 0.68 2.37 ± 0.68 3.74 ± 1.07 2.08 ± 0.70 2.36 ± 0.71 3.61 ± 0.86
F (N)
COP (mm)
ml: ap:
3.70 ± 4.13 5.17 ± 5.08
res:
5.02
res:
6.36
ml: ap:
3.28 ± 3.52 4.51 ± 4.48
res: ࢞:
4.93 −0.09
res: ࢞:
5.58 −0.78
ml: ap:
2.66 ± 2.88 3.92 ± 3.81
res: ࢞:
4.79 −0.23
res: ࢞:
4.74 −1.62
ml: ap: ml: ap:
3.32 ± 3.76 5.04 ± 3.92 3.89 ± 4.22 4.15 ± 4.04
res: ࢞: res: ࢞:
6.04 −0.32 5.69 −0.67
Effect of selected calibration approaches on the force and COP accuracy of the trials of the validation dataset in the walking area (see Fig. 1). With F, force; COP, center of pressure; ml, mediolateral; ap, anterior-posterior; vert, vertical direction; res, the resultant error; and ࢞, the difference with the standard calibration (negative value representing a lower error).
instrumented treadmills [13]. First, we examined whether the applicability of the protocol could be improved by including fewer or shorter measurements while reaching the same accuracy, or whether the accuracy improved by increasing the number of spots. The addition of extra spots was found to increase the COP accuracy compared with the 20 spots used by Collins et al. [13], while a reduction negatively affected the accuracy. In addition, accuracy generally decreased with a reduction of measurement duration, most prominently for left belt COP and right belt COPml , but not for all directions. For instance, the first part of the data contained the largest range and highest magnitude of vertical forces, so for this direction the accuracy did not improve with a longer duration. It was not examined whether increasing the measurement time would further increase the accuracy, however, the maximum measurement time (5s) seemed sufficient to exert a wide range of forces as the error leveled off, while at a longer duration fatigue is expected to negatively affect the exertion of high loads. The
optimal calibration dataset for all directions consisted of 30 spots per belt of 5s each, and improved the COP accuracy. Different approaches to construct the calibration matrix were examined. The local calibration reached the same accuracy as the standard calibration, indicating that crosstalk between the belts did not largely affect the force and COP accuracy. This is in agreement with the small crosstalk of below 1.5% measured for this treadmill [5]. Inclusion of offset and nonlinear terms slightly improved force accuracy, but negatively affected COP accuracy, which is in agreement with a previous study that found no accuracy improvement after addition of nonlinear terms [13]. After standard calibration, an inhomogeneous distribution of the COP error was found across the surface of the treadmill. These spatial differences could not have resulted from the specific order of the measurements or fatigue of the investigator applying the forces, because similar results were found in additional measurements the following day, while measuring in a different order
Please cite this article as: L.H. Sloot et al., Optimal calibration of instrumented treadmills using an instrumented pole, Medical Engineering and Physics (2016), http://dx.doi.org/10.1016/j.medengphy.2016.04.012
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Fig. 3. The effect of number of measurement spots and number of data samples on the resultant COP and force errors for the left and right belt (with blue indicating lower and red higher errors). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Please cite this article as: L.H. Sloot et al., Optimal calibration of instrumented treadmills using an instrumented pole, Medical Engineering and Physics (2016), http://dx.doi.org/10.1016/j.medengphy.2016.04.012
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Fig. 4. Spatial distribution of the RMSE COP for different calibration methods. The methods are without COP correction (A), with COP correction based on the method described by Schmiedmayer (B), or by Verkerke (C) and using the calibration matrix focused on the walking area (D). Indicated are the resultant (over anterior-posterior and medio-lateral direction) errors between treadmill and instrumented calibrator measurements (with green indicating lower and yellow higher errors). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) Table 3 Repeatability. Calibration method
Average RMSE per direction Day 1
Between day C1+V1 vs. C2+V2
Calibration data C1+V1 vs. C2+V1
F (N): ml: ap: vert: COP (mm): ml: ap: F (N): ml: ap: vert: COP (mm): ml:
Difference between days
Day 2
2.09 ± 0.50 2.46 ± 0.96 4.25 ± 1.22
2.53 ± 1.104 3.27 ± 1.49 6.18 ± 1.65
0.44 0.81 1.93
Fres (N):
2.14
2.09 ± 2.74 4.17 ± 3.71
1.73 ± 1.28 4.12 ± 2.15
0.36 0.05
COPres (mm):
0.36
2.09 ± 0.50 2.46 ± 0.96 4.25 ± 1.22
2.81 ± 0.96 2.15 ± 0.80 10.50 ± 3.49
0.72 0.31 6.25
Fres (N):
6.30
2.09 ± 2.74
2.63 ± 1.83
0.54
COPres (mm):
0.54
C1 refers to the calibration data set captured at day 1 that was used to calculate the calibration matrix and V1 the validation set captured at day 1 used to calculate the calibration matrix accuracy. Similarly, C2 and V2 refer to the calibration data and validation data captured at day 2. With F, force in N; COP, center of pressure in mm; res, resultant error; ml, mediolateral; ap, anterior-posterior; and vert, vertical direction.
(Supplementary material). It could have been caused by slight bending of the large force plates, which is less of a problem in ground mounted force plates. Still, error distributions have also been reported for these conventional force plates, with lowest errors in the center region [14,15]. Since the errors were not optimal within the walking area for our treadmill, the accuracy could be locally improved. A simple approach was to include only data from within this area, showing a significant increase in local COP accuracy that was larger than the variability measured between days. This could potentially be further increased by using a smaller metal plate which limited the distance to the belt edge. Alternatively, the nonlinearity in COP error could be reduced across the whole belt by correcting for the positional dependence. The method of Verkerke et al. [8] showed the best improvement across the belt surface (Fig. 4) and reduction within the walking
area. This could be interesting when subjects are not expected to limit their gait to a central area of the treadmill, for instance due to destabilizing perturbations. The optimization of the calibration methods using an instrumented calibrator only seemed to improve the overall accuracy to a limited extent, suggesting the maximal accuracy of this treadmill is approached given its inherent mechanical limitations. The accuracy reached after the different calibrations was within the range reported for most treadmills [13,26–28], although better (errors of 1.2–1.7 mm [29,30]) and worse (20–40 mm [8,31]) COP accuracies have also been reported. The differences between the various calibration methods in the calculated COP during gait (Fig. 2) were relatively small, with the largest difference around 5 mm for the medio-lateral direction on the left belt. Even so, average errors of around 2 and 4 mm in the different directions
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remained, although part of the error might be random and can be averaged away over multiple strides. It has been shown that shifts of 10 mm in the anterior-posterior COP can considerably alter the magnitude of joint kinetics, up to a 7% change in the ankle flexion moment, and 16% in knee and 8% in hip flexion moment [1,4,32]. A similar shift in the medio-lateral direction has been shown to reverse the pattern of ankle joint inversion-eversion moment [32]. This emphasizes the importance of calibration and, although the optimal calibration might depend on the treadmill and required accuracy for a measurement, this study provides several pointers to optimize the calibration protocol for a given instrumented treadmill. Future steps should not only focus on improvement of treadmill constructions, but also on decreasing the variability between calibration sessions to ensure an optimal and stable level of accuracy for a gait lab. This repeatability could benefit from further standardization of the calibration protocol, for instance by predefining a grid for the measurement spots and providing feedback on the exerted force to ensure a representative range of forces is included. In addition, the design of the instrumented pole could be improved, to enable exertion of representative forces and increase user friendliness, including limiting preparation time and designing an ergonomic grip. Furthermore, it would be interesting for quality assurance to examine the accuracy of a calibration matrix over time, by capturing different validation sets over a longer period of time. Lastly, the question remains whether static calibration provides the best transformation matrix for the treadmill outputs under experimental conditions, i.e. with a running belt. Future research should compare the accuracy of static with dynamic calibration techniques under these experimental conditions. Thus, the optimal calibration dataset consisted of 30 measurements per belt of 5s each. In addition, both correction for position dependence of COP error as well as its optimization within the walking area are found to be valuable additions to the standard calibration process. Potential improvements that should be further examined include standardization of force application, improvement of pole design, and applicability under experimental conditions. Conflict of interest The authors have no conflict of interest. Acknowledgments The authors would like to thank Bert Clairbois, Josien van den Noort, Adam Rozumalski, Pedro De Jesus Pereira Custódio and Linda van Gelder for their technical or measurement assistance. This study was financially supported by the Dutch Technology Foundation STW (#10733). None of the authors have competing interests. Ethical approval was provided by the local ethical committee of the Human Movement Faculty of the VU University. Supplementary materials Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.medengphy.2016.04. 012. References
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Please cite this article as: L.H. Sloot et al., Optimal calibration of instrumented treadmills using an instrumented pole, Medical Engineering and Physics (2016), http://dx.doi.org/10.1016/j.medengphy.2016.04.012